So. Rat #3 has made an appearance in the house. I finally just demanded the rental agency's contact info from my mom, so I could call them if she was going to insist on not doing it herself because she has some sense of...idk, pride or something that is wounded if she has to call the landlords to do anything. 
She's always hated having to tell the landlord about anything that needs fixing, even when we had a good one. I don't know why she's like this, I think it's just her sense of pride over being able to fix it all herself, but when you rent, you don't have to. They're legally required to take care of this shit for you! So there's no sense in doing
this to us or letting the rodents just have their way.
And yes, mom, there's plenty of things they can do. Exterminators can in fact get rid of a rat infestation. It might take a lot of work, but it can be done.
I know we killed the last two we saw, but just setting out traps and hoping that it works won't really solve the problem. There will always be more rats unless you find the source of them and make sure it stops.